Interrelationships Among Several Variables Reflecting Quantitative Thinking in Elementary School Children with Particular Emphasis Upon Those Measures Involving Metric and Decimal Skills

Abstract

Intercorrelations among several measures reflecting quantitative thinking tasks were found for subsamples of pupils at each of the first five grade levels in elementary schools in a middle-class suburban community in the greater Los Angeles area. One set of subsamples participated in an experimental instructional program emphasizing use of tactile, manipulative, and individual activity methodology in learning metric and decimal concepts, whereas a second set of subsamples of comparable ability levels took part in a traditionally taught program that did not stress manipulative activities. The appearance of substantial interrelationships among measures in the subsamples of pupils in the experimental program at the second, third, combined fourth-fifth, and fifth grade but for children in comparison groups at only the second and fourth grade levels suggested the existence of a general factor of quantitative thinking and the presence of greater degree of transfer and generalization of problem-solving capabilities to a variety of mathematics tasks for members of the experimental program than for those in a traditional program. For pupils in the first three grades, a standardized measure of the Piagetian construct of conservation failed to show much promise as a concurrently valid indicator of success in a number of mathematically related achievement measures. Relative to performance on a nationally standardized test in mathematics emphasizing traditional objectives and competencies, higher concurrent validity coefficients tended to be obtained for subsamples in the experimental program than for subsamples not in the program.

Learning With Real Machines or Diagrams: Application of Knowledge to Real-World Problems

“…First, researchers have studied hands-on learning in a variety of domains, such as mathematics, physics, biology, and chemistry (Fuller et al, 1979;Gabel & Shenvood, 1980;Selman, Sell, Michael, & Martois, 1976;Siegler, 1976). However, the results in one of these domains may not necessarily generalize to another.…”

“…Third, media are presented to students in a variety of learning situations (Fuller et al, 1979;Glasson, 1989;Selman et al, 1976). Often the instructional medium is confounded with the other aspects of the learning situation, such as the specific classroom and style of teaching or the particular learning activities that students engage in (e.g., hands-on vs. textbook, discovery vs. directed learning).…”